Talk:Juggernaut (Brick)
The mechanics behind Silent Resolve explain why Juggernaut "Damage Resistance" does not reduce damage by the displayed percentage. 00:21, June 16, 2010 (UTC)Cyke Diminishing returns The recent edit to the page claims the returns are not diminishing. But: *Level 1: Hp: 1000->1100 => 10% increase *Level 11: Hp: 2000->2100 => 5% increase While one could argue that each skill level does not give less than the previous, you do get less out of each subsequent skill investment. happypal (talk • ) 21:42, August 22, 2012 (UTC) :By that logic, any linear progression has diminishing returns. :This is the part that many people (including myself, in the past) misunderstand. Diminishing returns are defined as a decreasing output-per-unit-of-input as the total input increases. As an example, take planting seeds in a field. Each seed yields one tree. Eventually, however, the plants will begin fighting for food and light, and so not all of the seeds will grow, maybe you only get 0.8 trees per seed. As you crowd it more, maybe you only get 0.5 trees per seed. This is an example of diminishing returns. :So if the first level of Juggernaut gave you +10% effective health, then the next one gave +9%, then the next gave +8%, and so forth, that would mean it gives diminishing returns. :It's just a matter of understanding the term and applying concepts properly. 23:52, August 22, 2012 (UTC) ::The point remains that the more points you dump into the skill, the less useful each subsequent point will be. Maybe the term "diminishing return" does not apply correctly (arguably), but the fact remains you get less for each subsequent point invested in the skill. The article does not read that way. ::BTW, as a rule of thumb, in a level-based video game such as borderlands, yes, linear progression is diminishing returns. ::On the other end, geometric growth is constant return. Have you ever played a Final Fantasy? In Final Fantasy, every point put in strength increases damage by a fixed percent: ::*level 10->11: Damage 100->110 ::*level 200->201: Damage 2 000 000 -> 2 200 000 ::Anyways, I got some other things to concentrate on in the immediate future. Thanks for the overhaul. happypal (talk • ) 06:17, August 23, 2012 (UTC) :::I'm quite versed with the Final Fantasy universe, and I am pretty certain that not a single one of their games uses an exponential progression in their formulas. Citation needed on your claim there. The only game I'm aware of that does actually use exponential progression is Guild Wars. 10:03, August 23, 2012 (UTC) Fine, not outright Exponential, but FFX does use cubic growth: *http://www.gamefaqs.com/ps2/197344-final-fantasy-x/faqs/31381 Taking just the first part of the formula: "(Stat^3 ÷ 32) + 32" this creates: *10 => 63 *11 => 73 (+10 or +15%) *50 => 3874 *51 => 4177 (+303 or +7%) *100 => 31282 *101 => 32228 (+946 or +3%) So what is that, increasingly good returns? BTW, you state: "So if the first level of Juggernaut gave you +10% effective health, then the next one gave +9%, then the next gave +8%, and so forth, that would mean it gives diminishing returns." +X% compared to what? To the health you already have? Because that is exactly what it does. happypal (talk • ) 12:20, August 23, 2012 (UTC) :Any progression with a degree greater than 1 (quadratic, cubic, etc.) will indeed have increasing returns (and an exponential progression would have "accelerating returns"). As you just demonstrated, even a cubic progression ends up having your definition of "diminishing returns" (because the difference relative to the total value will always decrease), and in fact any polynomial progression will have that form of "diminishing returns." :To answer your second question: "+X%" compared to the initial value given. To reduce confusion from percentages, say you have an "effective health multiplier" stat that starts at 1, and each level of Juggernaut grants +0.1 to your health multiplier. You put in one rank, it returns 0.1 in your effective health multiplier stat. You put in another rank, it returns 0.1. Another rank, it returns 0.1. Each time, it returns the same amount. The return does not diminish, nor does it increase or accelerate. 14:32, August 23, 2012 (UTC) ::Yet, in the article, the return is defined as "survivability gain". By my book, the increase in survivability gets smaller by each level. ::Regardless, I think both you and I can agree that without a definition of what "return" is (which is what this disagreement is actually about), we can't really talk about whether or not there is a "Diminishing Return" ::However, the fact remains that all numbers aside, each subsequent level of this skill will not be as useful to the player as the previous level, and that is what counts. What really bothers me is the conclusion reached in the article: "Titans should put as many points as they wish in the skill", is just plain erroneous: A Titan with 2000 Hp will get less use out of +100 Hp than a Titan with 1000 Hp. That's just common sense. happypal (talk • ) 16:18, August 23, 2012 (UTC) :::Just to make sure we're on the same page here, the issue is that we can't agree on a definition of "diminishing returns" when one of the two of us is using a definition that has been in place in economic studies and numerical analysis since ancient Greek agriculture? 17:57, August 23, 2012 (UTC) :I perfectly understood what "diminishing returns" means, but if you are going to be a dick about it, here is what you are failing to see: :*Crop is a commodity. Crop you can buy, sell, trade etc. 100 Kernels of Corn will always be worth a 100 Kernels of Corn, regardless of if you currently have 5 or a million Kernels. Spend one seed, get one Kernel of crop; constant return. :*Hp Capacity is not a commodity though. It is just a bunch of single elements. It is a whole, a sum, that measures a rating of your survivability. You can't quantify the value of "+100 Hp capacity" without a reference to compare it to. If you have 500 Hp, then those "+100 Hp" will have a huge value to you, and give you +20% Survivability. On the other hand, if you already have 2000 Hp, then those "+100 Hp" will be worth nothing to you. A mere +5% increase in survivability. :Consequence: In terms of survivability gain, which, again, is what the article speaks of, yes, you do get diminishing returns. : :If you still aren't convinced, let's forget numbers and just try a little rhetoric. :*Imagine a field that does give you a constant return, and you had 1 000 000 seeds. If planting just one seed in that field gave you a return on investment, then by all logic, you'd plant all your seeds in that field, correct? After all: constant return means that if 1 seed gives you a return on investment, the 999 999 will give you the same return on investment. No point in ever stopping, right? :*Now imagine you could split all your skill points between Hardened (+12% health) and Safeguard (+8% shields), what would you do? If your answer isn't "I'd put ALL my points into a single skill", then that would mean there was a point at which you decided the return on investment was better on the other skill, ergo, a change of return, ergo, diminishing returns. QED. :happypal (talk • ) 20:54, August 23, 2012 (UTC) ::100 kernels of corn will always be worth 100 kernels of corn regardless of whether you have 5 kernels or a million kernels. 100 hit points will always be worth 100 hit points regardless of whether you have 5 hit points or a million hit points. Get hit for 1 damage, lose 1 hit point. ::Simply pretend that each hit point is a kernel of corn. When you get hit, people are stealing your corn kernels. If you have 500 kernels, then 100 more kernels is pretty substantial, relatively, giving you +20% corn. On the other hand, if you already have 2000 kernels, then those +100 kernels will be a mere +5% increase in harvest. ::Consequence: In terms of harvest gain, you get diminishing returns. :: ::Do not blur diminishing returns with multiplicative growth. When a final product is based upon two or more factors, it always benefits you to increase all of the factors simultaneously instead of focusing on one. If you have a stat X which is equal to Y × Z, doubling both Y and Z has a larger effect than tripling just one or the other. This is a separate concept from diminishing returns. 21:44, August 23, 2012 (UTC) :::Well played debunking my rhetoric. That's a good point you make. happypal (talk • ) 08:42, August 24, 2012 (UTC) You are correct about "linear growth means constant returns". You'll notice, for example, that neither Hardened nor Safeguard make any claims of diminishing returns. Also, you've forced me into deeper research of the definition of Diminishing Returns. Also TY for multiplicative growth explanation. I've learned something today, and I do thank you for it, as well as I feel bad about this conflict. So what is different about Juggernaut, and why am I being a such a douche about this? Because of the metric. From the beginning, There has been a claim that you could measure the effect of Juggernaut as if it gave extra health. The problem is that Juggernaut doesn't give you extra health, that's wishful thinking, and erroneous analysis. It reduces damage taken, (and improves survivability). Here is the data, as presented in the article, regarding what Juggernaut actually does: *Level 0, 1000 Damage: 1000 damage taken, 100.0% of damage taken. *level 1, 1000 Damage: 909 damage taken, 90.9% of damage taken. *Level 10, 1000 Damage: 500 damage taken, 50.0% of damage taken. *level 11, 1000 Damage: 476 damage taken, 47.6% of damage taken. Extra entry with 2000 Damage, to compare with a same initial damage of 1000. *Level 10, 2000 Damage: 1000 damage taken, 50.0% of damage taken. *level 11, 2000 Damage: 952 damage taken, 47.6% of damage taken. This gives us the following data. These are the correct measurements of Juggernaut's effects, and no matter how you measure it (absolute/percentage, relative to origin/previous), those are Diminishing Returns on investment, and the conclusion reached in the article, is erroneous: Take careful consideration into the amount of points put into Juggernaut. happypal (talk • ) 09:20, August 24, 2012 (UTC) :Ah, but it does give you extra health. You can literally pretend that it gives you extra health and you also receive a healing bonus. ::Example: You have 1000 health and 100% resistance. You get hit by a 200-damage attack and are healed for 50. The damage is halved by the resistance, so you're reduced to 900 health, and then are healed for 50 to reach 950 health (95% health). ::Now, pretend that it gives you +100% health and +100% healing. You have 2000 health, and get hit by a 200-damage attack and are healed for 50. The damage brings you from 2000 to 1800, and you then are healed by 100 (because the 50 had a +100% bonus) to reach 1900 health (95% health). :So not only does damage resistance indeed function exactly like percentage-bonus-health, but it also increases the relative effectiveness of healing because it requires more effort to steal your kernels of corn than it does to get them back ;). :Thank you for your calm deliberation on the subject, and let me know if this explanation requires further elaboration. 18:39, August 24, 2012 (UTC) ::That is a very interesting argument: It is perfectly accurate, and I agree with it. Yet, it doesn't debunk my point of view of diminishing reduction of damage argument either. This places us back to square 1: what is the metric? ::I need to break from the wiki for the week end (and rest from a pretty intense week actually). Thanks for putting up with me, and I'll get back to you Monday. happypal (talk • ) 21:31, August 24, 2012 (UTC) :::As a single number, the "reduction of damage" does have diminishing returns. However, that's not the statistic we're interested in. What matters in Borderlands is "how many hits does it take?" Damage reduction makes that number go up, and how high that number is is what matters to us, not how much less damage is being taken. 21:42, August 24, 2012 (UTC) Conclusion Ok, you have successfully convinced me that Juggernaut is constant return. Its mechanics are the same as, say Hardened. I still have one example regarding "amount of shots" that I want to get of my chest though, but I'm not trying to convince anyone anymore, just want it written for posterity: *You have 100 HP: *You meet enemy A, which deals 5 damage per shot with his SMG, and promptly kills you after 20 shots. *You decide to invest a point in Juggernaut/Hardened (both give +10% here). *Enemy you meet enemy A again, and this time, he kills you in 22 shots. *You still died, but your survivability went from "20 shots to 22 shots". Pretty good. *You decide you like the skill, and invest 10 points into it. *You meet enemy B, which deals 10 damage per shot with his SMG, and promptly kills you after 20 shots. *You decide to invest a point in Juggernaut/Hardened (10 -> 11) *Enemy you meet enemy B again, and this time, he kills you in 21 shots. *It looks like your survivability "only" went from "20 shots to 21 shots" :/ Now, my issue here is not about "diminishing returns" anymore (again, you have convinced me otherwise). It is about the sentence: "Titans should put as many points as they wish in the skill". This sentence really makes it sound as if a Titan should "Put as many points as possible into this skill". This really isn't sound advice, and is not given on any other skill. Plus, it is POV anyways. I will be removing it per "Opinion". Also, I am re-writting the paragraph to sound more like an explanation, rather than a scientific rebuttal (which feels very target btw...). happypal (talk • ) 13:17, August 27, 2012 (UTC) :Well, if the objective of a Titan is to take the maximum number of hits before going down, then he should indisputably maximize his investment in Juggernaut. Like any other skill, its worth depends on your goal. 18:55, August 27, 2012 (UTC) ::True, but also true of Hardened, Safeguard, Diehard, or Unbreakable. And also Blood Sport too. ::We generally avoid such COM specific notes in skills, or it just ends up being noise. We only do it when the COM can have very particular effect on the skill, such as Unbreakable with Titan. That or when we want to note the highest value a field can reach, such as Overload with a Heavy Gunner. In all other cases, it is usually deemed not interesting enough to warrant the note. happypal (talk • ) 19:45, August 27, 2012 (UTC) :::Phrasing it as "A Titan investing in Juggernaut can reduce his damage by nearly half (47.3%)" could work actually. Or something along those lines. happypal (talk • ) 19:52, August 27, 2012 (UTC) In game tooltip is inaccurate Having looked at this skill in the Unreal Editor for Borderlands, I discovered that although the tooltip claims you gain 10% damage reduction per skill points, internally that value is actually 12% per point invested. This obviously changes the math a little (100% damage reduction still means you take 50% damage as it's really 100% increased effective hit points). I'm prepared to rewrite the page accordingly but I'm not sure how I should handle pointing out the erroneous tooltip (quite a few other skills in the game have incorrect tooltips that I know of, so there's a 'how should we template this?' question here) Frightning Lightning (talk) 23:56, July 17, 2014 (UTC)